Recent advances in the design and fabrication of on-chip optical microresonators has greatly expanded their applications in photonics, enabling metrology, communications, and on-chip lasers. Designs for these applications require fine control of disp
ersion, bandwidth and high optical quality factors. Co-engineering these figures of merit remains a significant technological challenge due to design strategies being largely limited to analytical tuning of cross-sectional geometry. Here, we show that photonic inverse-design facilitates and expands the functionality of on-chip microresonators; theoretically and experimentally demonstrating flexible dispersion engineering, quality factor beyond 2 million on the silicon-on-insulator platform with single mode operation, and selective wavelength-band operation.
Superradiance is a cooperative phenomenon in quantum optical systems wherein the emission of photons from a quantum emitter is enhanced due to other quantum emitters coupling to the same electromagnetic mode. However, disorder in the resonant frequen
cies of the quantum emitters can prohibit this effect. In this paper, we study the interplay between superradiance, spectral disorder and dynamical modulation in a Tavis-Cumming model wherein all the emitters couple to a single resonant electromagnetic mode. As a consequence of the all-to-all coupling between the emitters, the presence of spectral disorder never prohibits the formation of a superradiant state over an extensive number of emitters. Furthermore, in such disordered systems, we show that a quantum control protocol modulating the resonant frequency of the optical mode leads to a multiplicative enhancement in the superradiance even in the limit of large number of emitters. Our results are relevant to experimental demonstration and application of superradiant effects in solid-state quantum optical systems such as color centers or rare-earth ions.
Inverse design of large-area metasurfaces can potentially exploit the full parameter space that such devices offer and achieve highly efficient multifunctional flat optical elements. However, since practically useful flat optics elements are large in
the linear dimension, an accurate simulation of their scattering properties is challenging. Here, we demonstrate a method to compute accurate simulations and gradients of large-area metasurfaces. Our approach relies on two key ingredients - a simulation distribution strategy that allows a linear reduction in the simulation time with number of compute (GPU) nodes and an efficient single-node computation using the Transition-matrix (T-matrix) method. We demonstrate ability to perform a distributed simulation of large-area, while accurately accounting for scatterer-scatterer interactions significantly beyond the locally periodic approximation, and efficiently compute gradients with respect to the metasurface design parameters. This scalable and accurate metasurface simulation method opens the door to gradient-based optimization of full large-area metasurfaces.
Non-Markovian effects are important in modeling the behavior of open quantum systems arising in solid-state physics, quantum optics as well as in study of biological and chemical systems. A common approach to the analysis of such systems is to approx
imate the non-Markovian environment by discrete bosonic modes thus mapping it to a Lindbladian or Hamiltonian simulation problem. While systematic constructions of such modes have been proposed in previous works [D. Tamascelli et al, PRL (2012), A. W. Chin et al, J. of Math. Phys (2010)], the resulting approximation lacks rigorous convergence guarantees. In this paper, we initiate a rigorous study of the convergence properties of these methods. We show that under some physically motivated assumptions on the system-environment interaction, the finite-time dynamics of the non-Markovian open quantum system computed with a sufficiently large number of modes is guaranteed to converge to the true result. Furthermore, we show that, for most physically interesting models of non-Markovian environments, the approximation error falls off polynomially with the number of modes. Our results lend rigor to numerical methods used for approximating non-Markovian quantum dynamics and allow for a quantitative assessment of classical as well as quantum algorithms in simulating non-Markovian quantum systems.
Matrix powering is a fundamental computational primitive in linear algebra. It has widespread applications in scientific computing and engineering, and underlies the solution of time-homogeneous linear ordinary differential equations, simulation of d
iscrete-time Markov chains, or discovering the spectral properties of matrices with iterative methods. In this paper, we investigate the possibility of speeding up matrix powering of sparse stable Hermitian matrices on a quantum computer. We present two quantum algorithms that can achieve speedup over the classical matrix powering algorithms -- (i) an adaption of quantum-walk based fast forwarding algorithm (ii) an algorithm based on Hamiltonian simulation. Furthermore, by mapping the N-bit parity determination problem to a matrix powering problem, we provide no-go theorems that limit the quantum speedups achievable in powering non-Hermitian matrices.
A transducer of single photons between microwave and optical frequencies can be used to realize quantum communication over optical fiber links between distant superconducting quantum computers. A promising scalable approach to constructing such a tra
nsducer is to use ensembles of quantum emitters interacting simultaneously with electromagnetic fields at optical and microwave frequencies. However, inhomogeneous broadening in the transition frequencies of the emitters can be detrimental to this collective action. In this article, we utilise a gradient-based optimization strategy to design the temporal shape of the laser field driving the transduction system to mitigate the effects of inhomogeneous broadening. We study the improvement of transduction efficiencies as a function of inhomogeneous broadening in different single-emitter cooperativity regimes and correlate it with a restoration of superradiance effects in the emitter ensembles. Furthermore, to assess the optimality of our pulse designs, we provide certifiable bounds on the design problem and compare them to the achieved performance.
Bound states arise in waveguide QED systems with a strong frequency-dependence of the coupling between emitters and photonic modes. While exciting such bound-states with single photon wave-packets is not possible, photon-photon interactions mediated
by the emitters can be used to excite them with two-photon states. In this letter, we use scattering theory to provide upper limits on this excitation probability for a general non-Markovian waveguide QED system and show that this limit can be reached by a two-photon wave-packet with vanishing uncertainty in the total photon energy. Furthermore, we also analyze multi-emitter waveguide QED systems with multiple bound states and provide a systematic construction of two-photon wave-packets that can excite a given superposition of these bound states. As specific examples, we study bound state trapping in waveguide QED systems with single and multiple emitters and a time-delayed feedback.
Understanding dynamics of localized quantum systems embedded in engineered bosonic environments is a central problem in quantum optics and open quantum system theory. We present a formalism for studying few-particle scattering from a localized quantu
m system interacting with an bosonic bath described by an inhomogeneous wave-equation. In particular, we provide exact relationships between the quantum scattering matrix of this interacting system and frequency domain solutions of the inhomogeneous wave-equation thus providing access to the spatial distribution of the scattered few-particle wave-packet. The formalism developed in this paper paves the way to computationally understanding the impact of structured media on the scattering properties of localized quantum systems embedded in them without simplifying assumptions on the physics of the structured media.
The ability to shape photon emission facilitates strong photon-mediated interactions between disparate physical systems, thereby enabling applications in quantum information processing, simulation and communication. Spectral control in solid state pl
atforms such as color centers, rare earth ions, and quantum dots is particularly attractive for realizing such applications on-chip. Here we propose the use of frequency-modulated optical transitions for spectral engineering of single photon emission. Using a scattering-matrix formalism, we find that a two-level system, when modulated faster than its optical lifetime, can be treated as a single-photon source with a widely reconfigurable photon spectrum that is amenable to standard numerical optimization techniques. To enable the experimental demonstration of this spectral control scheme, we investigate the Stark tuning properties of the silicon vacancy in silicon carbide, a color center with promise for optical quantum information processing technologies. We find that the silicon vacancy possesses excellent spectral stability and tuning characteristics, allowing us to probe its fast modulation regime, observe the theoretically-predicted two-photon correlations, and demonstrate spectral engineering. Our results suggest that frequency modulation is a powerful technique for the generation of new light states with unprecedented control over the spectral and temporal properties of single photons.
We study the scattering of photons from periodically modulated quantum-optical systems. For excitation-number conserving quantum optical systems, we connect the analytic structure of the frequency-domain N-photon scattering matrix of the system to th
e Floquet decomposition of its effective Hamiltonian. Furthermore, it is shown that the first order contribution to the transmission or equal-time N-photon correlation spectrum with respect to the modulation frequency is completely geometric in nature i.e. it only depends on the Hamiltonian trajectory and not on the precise nature of the modulation being applied.
